ABSTRACT
Recent availability of small inexpensive low power GPS receivers and techniques for finding relative coordinates based on signal strengths, and the need for the design of power efficient and scalable networks, provided justification for applying position based routing methods in ad hoc networks. A number of such algorithms were developed in last few years, in addition to few basic methods proposed about fifteen years ago.
This article surveys known routing methods, and provides their taxonomy in terms of a number of characteristics: loop-free behavior, distributed operation (localized, global or zonal), path strategy (single path, multi-path or flooding based), metrics used (hop count, power or cost), memorization (memoryless or memorizing past traffic), guaranteed delivery, scalability, and robustness (strategies to handle the position deviation due to the dynamicity of the network).
We also briefly discuss relevant issues such as physical requirements, experimental design, location updates, congestion, scheduling node activity, topology construction, broadcasting and network
1. INTRODUCTION
Mobile ad hoc networks (often referred to as MANETs) consist of wireless hosts that communicate with each other in the absence of a fixed infrastructure. They are used in disaster relief, conference and battlefield environments, and received significant attention in recent years. A class of wireless ad hoc networks that is currently subject of intensive research is sensor network. Wireless networks of sensors are likely to be widely deployed in the near future because they greatly extend our ability to monitor and control the physical environment from remote locations and improve our accuracy of information obtained via collaboration among sensor nodes and online information processing at those nodes.
Networking these sensors (empowering them with the ability to coordinate Ã‚Â¦amongst themselves on a larger sensing task) will revolutionize information gathering and processing in many situation. Rooftop networks are not mobile, but are deployed very densely in metropolitan areas (the name refers to an antenna on each building's roof, for line-of-sight with neighbors) as an alternative to wired networking. Such a network also provides an alternative infrastructure in the event of failure of the conventional one, as after a disaster. A routing system that self-configures (without a trusted authority to configure a routing hierarchy) for hundreds of thousands of such nodes in a metropolitan area represents a significant scaling challenge.
Commercial examples of static ad hoc networks include Metricom Ricochet and Nokia Rooftop systems. Other similar contexts are wireless local area networks, packet radio networks, home and office networks, spontaneous networks etc.
. Routing is performed by a scheme that is generally classified as position-based scheme. The distance between neighboring nodes can be estimated on the basis of incoming signal strengths. Relative coordinates of neighboring nodes can be obtained by exchanging such information between neighbors .

2. UNIT GRAPH REPRESENTATION
A widely accepted basic graph-theoretical model for all mentioned networks is the unit graph model, defined in the following way.

Radius
Figure 1. Unit graph representation of multi-hop wireless network
Two nodes A and B in the network are neighbors (and thus joined by an edge) if the Euclidean distance between their coordinates in the network is at most R, where R is the transmission radius which is equal for all nodes in the network. Variation of this model include unit graphs with obstacles (or subgraph of unit graph), minpower graphs where each node has its own transmission radius and links are unidirectional or allowed only when bidirectional communication is possible. However, no credible research was done in literature on any other model other than unit graph model . Figure 1 gives an example of a unit graph with transmission radius as indicated. Because of limited transmission radius, the routes are normally created through several hops in such multi-hop wireless network. For most algorithms reviewed here, the unit graph model is used in experiments, while the algorithm itself may be applied for arbitrary graph. In this article we consider the routing task, in which a message is to be sent from a source node to a destination node in a given wireless network. The task of finding and maintaining routes in sensor and mobile networks is nontrivial since host mobility and changes in node activity status cause frequent unpredictable topological changes. The destination node is known and addressed by means of its location.
3. POSITION-BASED ROUTING PROTOCOLS TAXONOMY
Macker and Corson listed qualitative and quantitative independent metrics for judging the performance of mobile ad hoc networks routing protocols. Desirable qualitative properties include: distributed operation, loop-freedom (to avoid a worst case scenario of a small fraction of packets spinning around in the network), demand-based operation, and 'sleep' period operation (when some nodes become temporarily inactive). Our goal is to provide a taxonomy of existing position based routing algorithms in light of qualitative characteristics listed below.
a) Loop-freedom: The proposed routing protocols should be inherently loop-free, to
avoid timeout or memorizing past traffic as cumbersome exit strategies. Proposed
algorithms are therefore classified as having or not having loop free property.
b) Distributed operation: Localized algorithms are distributed algorithms that
resemble greedy algorithms, where simple local behavior achieves a desired global
objective. In a localized routing algorithm, each node makes decision to which neighbor
to forward the message based solely on the location of itself, its neighboring nodes, and
destination. Non-localized algorithms can be classified as global or zonal ones. In a
global routing algorithm, each node is assumed to know the position of every other node
in the network. In addition, since nodes change between active and sleep periods, the
activity status for each node is also required.
When such global knowledge is available, the routing task becomes equivalent to the shortest path problem, if hop count is used as main performance metrics. If power or cost metrics are used instead, the shortest weighted path algorithm may be applied. Between the two extremes is the zonal approach, where network is divided into zones, with localized algorithm applied within each zone, and shortest path or other scheme applied for routing between zones. Clearly, localized algorithms are preferred if they can nearly match the performance of non-localized ones. An expanded locality is sometimes considered. For example, if two hop neighbors are included, the algorithm is classified as 2-localized.
c) Path strategy: The shortest path route is an example of a single path strategy, where
one copy of the message is in the network at any time. Arguably, the ideal localized
algorithm should follow a single path. On the other extreme are flooding based
approaches, where message is flooded through the whole network area (broadcasting solves routing, and in high mobility scenario this could be optimal solution). The 'compromise' is multi-path strategy, that is route composed of few single recognizable paths. Some algorithms are combinations of two strategies, and are appropriately labeled (e.g. single-path/flooding, single-path/multi-path).
d) Metrics: The metrics that is used in simulations normally reflects the goal of
designed algorithm, and is naturally decisive in the route selection. Most routing
schemes use hop count as the metrics, where hop count is the number of transmissions
on a route from a source to destination. This choice of metric agrees with the
assumption that nodes cannot adjust (that is, reduce) their transmission radii in order to
reach desired neighbor with minimal power. It also assumes that delay is proportional to
hop count (when the impact of congestion is not significant), and that the (both energy
and bandwidth) cost of starting communication with neighbor is considerable supported.
However, if nodes can adjust their transmission power (knowing the location of their neighbors) then the constant metric can be replaced by a power metric that depends on distance between nodes. The goal is to minimize the energy required per each routing task. However, some nodes participate in routing packets for many source-destination pairs, and the increased energy consumption may result in their failure. Thus pure power consumption metric may be misguided in the long term, and longer path that passes through nodes that have plenty of energy may be a better solution. The cost metric (a rapidly increasing function of decreasing remaining energy at node) is used with the goal of maximizing the number of routing tasks that network can perform.
e) Memorization: Solutions that require nodes to memorize route or past traffic are
sensitive to node queue size, changes in node activity and node mobility while routing is
ongoing (e.g monitoring environment). It is better to avoid memorizing past traffic at
any node, if possible. However, the need to memorize past traffic is not necessarily a
demand for significant new resources in the network for several reasons. First, a lot of
memory space is available on tiny chips. Next, the memorization of past traffic is
needed for short period of time, while ongoing routing task is in progress, and therefore
after a timeout outdated traffic can be safely removed from memory. Finally, the
creation of Quality-of-Service (QoS) path, that is, path with bandwidth, delay, and
connection time requirements, requires that the path is memorized in order to optimize
the traffic flow and satisfy QoS criteria. This certainly includes the use of the best path
found in the search process. Once destination is reached, the optimal path can be reported back to source.
f) Guaranteed message delivery: Delivery rate is the ratio of numbers of messages received by destination and sent by senders. The primary goal of every routing scheme is to delivery the message, and the best assurance one can offer is to design routing scheme that will guarantee delivery. Wireless networks normally use single frequency communication model where a message intended for a neighbor is heard by all other neighbors within transmission radius of sender. Collisions are normally occurring in medium access schemes mostly used. The guaranteed delivery property assumes the application of an ideal, collision free, medium access scheme, such as time division multiple access, or acknowledgement/retransmission scheme that is assumed to be always successful otherwise.
g) Scalability: The routing algorithms should perform well for wireless networks with arbitrary number of nodes. Sensor and rooftop networks, for instance, have hundreds or thousands of nodes. Scalable single-path strategies, such as shortest-path, have 0( n ) overhead, where n is the number of nodes in the network. While other characteristics of each algorithms are easily detected, scalability is sometimes judgmental, and/or dependent on performance evaluation outcome. We shall apply a simplified criterion, that a routing scheme is scalable if it is loopfree, localized, and single-path. Note that, several schemes, are proved to guarantee the messages delivery (and to be loop free) in the static case.
It is not clear how these schemes handle loops and perform delivery in the case of node mobility. We name these loops due to the position of some nodes as mobility-caused loops. These loops are in general temporary loops that appear because some nodes move in a position that causes the packet to loop. This situation cannot be easily detected because it arises after the direction for packet has been chosen.In this work we classify as loop free and delivery guarantee, as traditionally done, all schemes that are proved to be loop free and which guarantee the message delivery, even if they are not proved for the mobility-caused loops.
h) Robustness: The use of nodes' position for routing poses evident problems in terms
of reliability. The accuracy of destination position is an important problem to consider.
In some cases the destination is a fixed node (such as monitoring center known to all
nodes, or the geographic area that is monitored), some networks are static which makes

the problem straightforward, while the problem of designing location updates schemes to enable efficient routing in mobile ad hoc network appears to be more difficult than routing itself.
For small networks, in the absence of any useful information about destination location (that is, a clever location update scheme), the following simple strategy can be applied. If message is reasonably 'short', it can be broadcasted (that is, flooded), using an optimal broadcasting scheme. If message is relatively 'long' then destination search can be initiated, which is a task of broadcasting short search message. Destination then reports back to source by routing a short message containing its position. The source then is able to route full message toward accurate position of destination.
However, in large networks, the algorithms that assume that the position of destination is 'reasonably' accurate are not able to deal with eventual position deviation, and impose high mobility tracking overhead. More robust and scalable routing algorithms must, by design, be able to cope with the network dynamicity or can have backup strategies that allow to reach a node even when the node deviated from the known position. Another aspect of robust algorithms is their ability to deliver message when communication model deviates from unit graph, due to obstacles or noise.
4. POSITION BASED ROUTING SCHEMES
Performance of most algorithms surveyed in this paper will be discussed in terms of delivery rates and hop counts obtained in simulations, for graphs of various densities (measured by average degrees, that is, average number of neighbors of each node). This suffices for single-path strategies, but is misleading for flooding based or multi-path ones. Due to limited battery power, the communication overhead must be minimized if number of routing tasks is to be maximized. Purely proactive methods that maintain routing tables with up-to date routing information or global network information at each node are certainly unsatisfactory solution, especially when node mobility is high with respect to data traffic. For instance, shortest path based solutions are too sensitive to small changes in local topology and activity status (the later even does not involve node movement). Since localized algorithm should compete with the best (shortest path) algorithm the flooding rate was introduced as a measure of communication overhead. Flooding rate is the ratio of the number of message transmissions and the shortest possible hop count between two nodes. Each transmission in multiple routes is counted, and a message can be sent to all neighbors with one transmission. Note that the cost of location updates is not counted in the flooding rate, although it should be added to the total communication overhead.
We can distinguish five main classes of existing position based routing schemes:
Â¢ Basic Distance, Progress, and Direction Based Methods
Â¢ Partial Flooding and Multi-Path Based Path Strategies
Â¢ Depth First Search Based Routing with Guaranteed Delivery
Â¢ Nearly Stateless Routing with Guaranteed Delivery
Â¢ Power and Cost Aware Routing

5. BASIC DISTANCE, PROGRESS ,AND DIRECTION BASED
METHODS
Given a transmitting node S, the progress of a node A is defined as the project and implimentationion onto the line connecting S and the final destination.of the distance between S and the receiving node A neighbor is in forward direction if the progress is positive (for example, for transmitting node S and receiving nodes A, C and F in Fig. 1); otherwise it is said to be in backward direction (e.g. nodes B and E in Fig. 1). Basic Distance, Progress, And Direction Based Methods use these concepts to select among neighbors the next routing step. Schemes as the Random Progress Method ,Most Forward within Radius , Nearest Forward Progress ,the Greedy Scheme , the Nearest Closer and all its variants (the 2-Hop Greedy Method the Alternate Greedy method ,the Disjoint Greedy method, and GEDIR ), and the Compass Routing method fall in this class. In the random progress method , packets destined toward D are routed with equal probability towards one intermediate neighboring node that has positive progress. The rationale for the method is that, if all nodes are sending packets frequently, probability of collision grows with the distance between nodes (assuming that the transmission power is adjusted to the minimal possible), and thus there is a trade-off between the progress and transmission success.

Figure 1. Positive and negative progress: C, A, F are in forward direction, with a positive progress (for example, A 'D < SD): nodes B and E are in backward direction, with a negative progress.
Takagi and Kleinrock proposed MFR (most forward within radius) routing algorithm, in which packet is sent to the neighbor with the greatest progress (e.g. node A in Fig. I).. MFR is probed to be a loop-free algorithm . MFR is the only progress-based algorithm competitive in terms of hop count.

In Nearest Forward Progress method is modified by proposing to adjust the transmission power to the distance between the two nodes. In this scheme, packet is sent to the nearest neighboring node with forward progress .
In 1987, Finn proposed, the greedy scheme as variant of random progress method, which 'allows choosing as successor node any node, which makes progress toward the packet's destination'. The optimal choice would be possible only with the complete topological knowledge of the network.. To bypass this problem, Finn adopted the greedy principle: select the node closest to the destination..When none of neighboring nodes is closer to the destination than current node C, Finn [F] proposes to search all n-hop neighbors (nodes at distance at most n hops from current node, where n is network dependent parameter) by flooding the nodes until a node closer to destination than C is found. The algorithm has non-trivial details and does not guaranty delivery, nor optimize flooding rate. The author argued that his algorithm has no loops, since it always forces message to make a step closer to the destination.
A variant of greedy algorithms, called GEDIR, is proposed. In this variant, the message is dropped if the best choice for a current node is to return the message to the node the message came from. It increases delivery rate by prolonging failure. The same criterion can be applied to MFR method. Greedy routing was applied as part of other routing schemes. GEDIR is often used as basic ingredient in other routines. For instance, it is used in several location update schemes, such as quorum based and home agent based schemes The MFR and greedy methods, in most cases, provide the same path to destination.Simulation in [SL2] revealed that nodes in greedy and MFR methods select the same forwarding neighbor in over 99% of cases, and, in the majority of the cases, the whole paths were identical. When successful, hop counts of greedy and MFR methods nearly match the performance of the shortest path algorithm.

6. PARTIAL FLOODING AND MULTI-PATH BASED PATH
STRATEGIES
In directional flooding-based routing methods, a node A transmits a message m to several neighbors whose direction (looking from A) is closest to the direction of destination D. In order to control flooding effect, flooding based method require nodes to memorize past traffic, to avoid forwarding the same message more than once. Distance routing effect algorithm for mobility (DREAM),Location aided routing(LAR) belong to this class. Flooding can be partial because it is directed towards nodes in a limited sector of the network (e.g. in DREAM or in LAR) or because it is stopped after a certain number of hops (e.g. in flooding GEDIR family of schemes). Moreover, partial flooding can be used only for path discovery purpose (e.g. LAR) or for packet forwarding (e.g. DREAM).
In DREAM protocol, m is forwarded to all neighbors whose direction belongs to the selected range, determined by the tangents from A to the circle centered at D and with radius equal to a maximal possible movement of D since the last location update. DREAM algorithm is a proactive protocol that uses a limited flooding of location update messages.
In the location aided routing (LAR) algorithm the request zone (the area containing the circle and two tangents)is fixed from the source, and nodes, which are not in the request zone, do not forward a route request to their neighbors. In LAR scheme- 2 the source or an intermediate node A will forward the message to all nodes that are closer to the destination than A. The control part of LAR protocol is, essentially, restricted to the request zone. Therefore all nodes inside an area receive the routing packet, and the algorithm is therefore of partial flooding nature, causing excessive flooding rates .
A different approach using flooding and multipath routing is the one taken in Terminode routing . Terminode routing addresses by design the following objectives: scalability (both in terms of the number of nodes and geographical coverage); robustness; collaboration and simplicity of the nodes. This routing scheme is a combination of two protocols called Terminode Local Routing (TLR) and Terminode Remote Routing (TRR). TLR is a mechanism that allows to reaching destinations in the vicinity of a terminode and does not use location information for making packet forwarding decisions. TRR is used to send data to remote destinations and uses

7. DEPTH FIRST SEARCH BASED ROUTING WITH GUARANTEED DELIVERY
Single-path strategies that guarantee delivery of the message to the destination are very relevant for supporting loss sensitive traffic. Geographic Routing Algorithm and the Depth First Search Based Algorithm schemes are based on this concept.
Jain, Puri and Sengupta proposed one such strategy called geographic routing algorithm (GRA), and it requires nodes to partially store routes toward certain destinations in routing tables. GRA applies greedy strategy in forwarding messages. However, sometimes node S may discover that it is closer to the destination D than any of its neighbors. That is, the packet may be 'stuck' at S. Under this condition, it starts the route discovery protocol. The route discovery finds a path from S to D and updates the routing tables toward D at any node on the path, with this information. After that the route discovery protocol is successfully completed, the stuck packet can be routed from Sto D.
The authors propose two route discovery strategies: breadth first search (which is equivalent to flooding) and depth first search (DFS). DFS yields a single acyclic path from S to D. Each node puts its name and address on the route discovery packet p. Then it forwards p to a neighbor who has not seen p before. This neighbor is one of all the neighbors which minimize d(S,y)+d(y,D), where d(x,y) is Euclidean distance between nodes x and y. If a node has no possibilities to forward the packet, it removes its name and address from the packet and returns the packet to the node from which it originally received it. Route discovery packets are kept for some time. If a node receives twice the same packet, it refuses it. The authors investigate routing table sizes and present methods for taking into account positional errors, node failures and mobility.
Another depth first search based algorithm has been independently proposed in Gateway DFS .The algorithm does not use routing tables, and instead message follows the whole depth first search path from S to D. Next, each node S minimizes d(S, D), and therefore the algorithm is equivalent to greedy method whenever it exists a node closer to D than S. For dense graphs most of t he paths generated by this method are the same as the paths obtained by the greedy method. The
1 T

authors discuss also the application of this method for the creation of quality-of-service (QoS) paths, that is, paths that satisfy delay and bandwidth criteria. In particular, they propose to use, as criterion, the connection time, which is time node S predicts to have link with any of its neighbor based on speed and direction of movements of S and its neighbor. In a simplified model considered in gateway DFS delay can be decomposed into propagation delay proportional to the hop count, and demand for additional bandwidth. In this model, edges with no sufficient bandwidth are simply ignored in the process. Additionally, the delay criterion reduces the search to finding a path with hop count no longer than a given maximum. When this maximum is reached, the greedy forwarding stops and the route discovery message is returned back in order to search another branch that might have shorter path. The nodes which remain on the created path memorize the forwarding and previous node on the path. When the so created path reaches the destination D, D can report it back to S along the path itself, and S can start sending to D. The algorithm can be evaluated in terms of length of route discovery path and length of created route.

8. NEARLY STATELESS ROUTING WITH GUARANTEED
DELIVERY
Nearly Stateless Routing with Guaranteed Delivery are schemes where nodes maintain only some local information to perform routing. The Face Routing and GFG (Greedy-Face-Greedy) schemes were described by Bose, Morin, Stojmenovic and Urrutia subsequently improved by applying dominating set concept and adding a shortcut 2-hop procedure. Recently, Barriere, Fraigniaud, Narayanan and Opatrny made them robust against intereferences. Karp and Kung transformed GFG algorithm into GPSR (Greedy Perimeter Stateless Routing) protocol by including IEEE 802.11 medium access control scheme. They experimented with mobile nodes moving according to a random waypoint model. The routing protocol traffic generated by GPSR was constant as mobility increased. Therefore the scalability seems to be the major advantage of this class of algorithms over source based protocols.
In order to ensure message delivery, the face algorithm constructs planar and connected so-called Gabriel subgraph of the unit graph, and then applies routing along the faces of the subgraph (e.g. by using the right hand rule) that intersect the line between the source and the destination. If a face is traversed using the right hand rule then a loop will be created, since face will never be existed .Forwarding in right hand rule is performed using directional approach. To improve the efficiency of the algorithm in terms of routing performance, face routing can be combined with greedy routing to yield GFG algorithm. Routing is mainly greedy, but if a mobile host fails to find a neighbor closer than itself to the destination, it switches the message from 'greedy' state to 'face' state.
Nearly stateless schemes are likely to fail if there is some instability in the transmission ranges of the mobile host. Instability in the transmission range means that the area a mobile host can reach is not necessarily a disk and the range can vary between r=(l-D)R and R, D>0. Barriere, Fraigniaud, Narayanan and Opatrny considered such kind of instability, and proposed this model as a generalization of unit graph. With this model they are able to handle the unstable situations where nodes may or may not communicate directly. This situation occurs if there are obstacles (e.g. buildings, bad weather) that disrupt the radio transmission.
9. POWER AND COST AWARE ROUTING
Hop count was traditionally used to measure energy requirement of a routing task, thus using constant metric per hop. However, if nodes can adjust their transmission power (knowing the location of their neighbors) then the constant metric can be replaced by a power metric that depends on distance between nodes. While the computational power of the devices used in the network is rapidly increasing, the lifetime of batteries is not expected to improve much in the future. We see a clear need for improvement in power consumption in existing routing algorithms. Schemes that combine position based and power/cost aware routing are proposed.
Rodoplu and Meng proposed a general model where the power consumption between two nodes with distance d is given by u(d)=dAk+c for some constants K and c, and describe several properties of power transmission that are used to find neighbors for which direct transmission is the best choice in terms of power consumption.
The investigation of energy consumption of existing IEEE 802.11 based ad hocnetwork interfaces shows that the constant c cannot be ignored (although most articles- in literature assume c=0). In other words, energy required to start up communication, which includes energy lost due to collisions, retransmissions and acknowledgements, is relatively significant. Protocols using any kind of periodic hello messages, frequently used in ad hoc network literature, are extremely energy inefficient, since energy and bandwidth metric cannot be equated.
Rodoplu and Meng also described a shortest weighted path based algorithm for finding power optimal routes from any source to a given fixed destination. They first construct power optimal enclosure graph rooted at each destination. However, assume c=0, and their constructions and proofs are not applicable for the case c>0. Therefore they do not improve of results if the realistic model with c>0 is considered.
Pure power consumption metric may be misguided in the long term : Some nodes participate in routing packets for many source-destination pairs, and the increased energy consumption may result in their failure. A longer path that passes through nodes that have plenty of energy may be a better solution, if the primary goal is to maximize the number of routing tasks the network can perform, that is, network life.

The localized cost efficient routing algorithm can be described as follows. If destination is one of neighbors of node B currently holding the packet then the packet will be delivered to D. Otherwise, B will select one of its neighbors A which will minimize c(A)=f(A)(l+s/R). The algorithm proceeds until the destination is reached, if possible, or until a node fails to find better forwarding neighbor than previous node on the path.
Power and cost are combined into a single metrics in order to choose power efficient paths among cost optimal ones. Longer paths via nodes with lot of energy will reduce a lot of power to the overall network. All proposed combinations shortest power cost path, route redirect are variations of the product of power and cost metrics .In multi-path route redirect algorithm, messages are redirected through any intermediate node that saves power or reduces cost. However, multi-path transmission in effect increases the power and cost, contrary to the design goals.
Li, Aslam and Rus discussed online power-aware routing in large wireless ad hoc networks for applications where the message sequence is not known. The goal is to optimize the lifetime of the network. They showed that online power aware routing (where incoming routing tasks are not known) does not have a constant competitive ratio to the off-line optimal algorithm (which is aware of all routing tasks). They developed an approximation algorithm that has a good competitive ratio, and selects the path with maximal minimal fraction of remaining power after the message is transmitted. The metrics used to measure that fraction is equivalent to power-cost metrics. The algorithm repeatedly calls Dijkstra's shortest path algorithm with tighter demands, removing all edges that excess preset threshold z, until source and destination are disconnected.

10. OTHER RELEVANT ISSUES IN ROUTING
The experimental design to evaluate routing schemes has some issues that required clarification. There was a tendency to compare hop count in proposed schemes against flooding instead of the shortest path and to ignore flooding rate. Also, transmission radius was used as independent variable, hiding graph density. Good results in many experiments were obtained by varying transmission range so that obtained graphs were all sparse or all dense, whichever way better results emerged. The average degree was proposed as independent variable, and was first applied in experimenting with position based routing schemes. To generate random unit graphs, each of n nodes is initially chosen by selecting its x and y coordinates at random in an interval [0,m). In order to control the initial average node degree k (that is, the average number of neighbors), all n(n-l)/2 (potential) edges in the network are sorted by their length, in increasing order. The radius R that corresponds to chosen value of k is equal to the length of nk/2-th edge in the sorted order. The parameter m is used in power aware routing, and can be fixed if hop count metric is used.
The network organization problem in wireless ad hoc and sensor networks received growing attention recently. Bluetooth is an emerging standard for short range wireless communication and networking. According to the standard, when two Bluetooth devices discover each other, one of them assumes the role of master and the other becomes slave. A master with up to seven slaves defines a piconet (each node is master for only one such piconet). Collection of piconets defines scatternet. The problem of scatternet formation to enable Bluetooth-based ad hoc networks was investigated recently.
Ad hoc routing requires that nodes cooperate to forward each others' packets through the network. This means that throughput available to each single node's applications is limited not only by the raw channel capacity, but also by the forwarding load imposed by distant nodes. This effect could seriously limit the usefulness of ad hoc routing. Gupta and Kumar estimated per node capacity in ad hoc network. If node density is constant and route length grows as 0( n ), where n is the number of nodes in the network, then end to end throughput available to each node is 0(1/ n ). Thus it approaches zero as the number of nodes increases. On the other hand, if average hop

count does not increase with network size (that is, most communication remains local), per node throughput remains constant.
IEEE 802.11 defines two primary modes of operation for a wireless network interface: idle state and sleep state. A node in idle state is active, and can react to ongoing traffic by switching to receive or transmit mode. A node in sleep state, however, cannot be activated by neighbors, and can return to idle state only on its own, based on preset timer. Feeney and Nillson and MIT researchers concluded that the idle power consumption is nearly as large as that of receiving data. Nodes in ad hoc network spend about 20% more energy when receiving than when idle, and about 60% more energy in transmit than in idle mode. The error margin here is not small, as exact number depends on the equipment and defers in published articles, but rounded numbers given here are sufficient for problem description. A node in idle mode spends about 15-30 times more energy than if it is in sleep mode. Therefore it is most important to have as many as possible sleeping nodes in the network. The active nodes should be connected and should provide basic routing and broadcasting functionalities.
n

11. CONCLUSION
The successful design of localized single-path loop-free algorithms with guaranteed delivery is encouraging start for future research. The search for localized routing methods that have excellent delivery rates, short hop counts, small flooding ratios and power efficiency is far from over. Since the battery power is not expected to increase significantly in the future and the ad hoc networks, on the other hand, are booming, power aware routing schemes need further investigation. In Quality-of-Service applications, memorization does not appear to require additional resources and is therefore acceptable. However, the research on Quality-of-Service position based routing is scarce and will receive more attention in the future.
12. FUTURE SCOPE
Further research is needed to identify the best global positioning system based routing protocols for various network contexts. These contexts include nodes positioned in three-dimensional space and obstacles, nodes with unequal transmission powers, or networks with unidirectional links. One of the future goals in designing routing algorithms is adding congestion considerations, that is, replacing hop count performance measure by end-to-end delay. Algorithms need to take into account the congestion in neighboring nodes in routing decisions. Finally, the mobility caused loop needs to be further investigated and solutions to be found and incorporated to position based routing schemes.